Python simulation of a catalytic packed bed plug flow reactor (PFR) for the partial oxidation of methanol to formaldehyde.
Based on the Imperial College London Reaction Engineering group design project (Group 20, 2025).
CH₃OH + ½O₂ → HCHO + H₂O (desired)
HCHO + ½O₂ → CO + H₂O (undesired — suppressed by design)
Target: 100 tonnes/day formaldehyde · Optimal design: 640 K isothermal · 0.5 m tubes · 23,000 tubes
| Module | Contents |
|---|---|
kinetics.py |
Power law model (empirical, regression fitted) and LHHW model (Deshmukh et al. 2005) |
pfr.py |
Packed bed PFR: material balance + energy balance + Ergun pressure drop |
analysis.py |
Temperature & length sensitivity, flammability limits, SQP optimisation |
git clone https://github.com/defnalk/formaldehyde-reactor.git
cd formaldehyde-reactor
pip install -r requirements.txtfrom reactor import PackedBedPFR, ReactorAnalysis
# Isothermal simulation at optimal conditions
pfr = PackedBedPFR(kinetics="LHHW", mode="isothermal", T_isothermal=640)
res = pfr.simulate(L=0.5)
print(f"HCHO yield: {res['yield_HCHO']:.1%}")
print(f"Selectivity: {res['selectivity']:.1%}")
print(f"MeOH conversion: {res['conversion']:.1%}")
print(f"Outlet pressure: {res['P'][-1]:.3f} atm")
# Temperature sensitivity sweep
import numpy as np
ra = ReactorAnalysis()
sens = ra.temperature_sensitivity(np.linspace(580, 700, 20), L=1.0)
# SQP optimisation
opt = ra.sqp_optimise()
print(f"Optimal L={opt['optimal_L']}m, T={opt['optimal_T']}K")python examples/full_simulation.pyGenerates a 4 panel figure:
Panels:
- A, Isothermal molar flow profiles (LHHW, 640 K) showing CH₃OH consumed, HCHO produced
- B, Adiabatic temperature profile, steep rise near inlet, then plateau as reactants deplete
- C, Yield and selectivity vs. temperature, identifies 640 K as optimal
- D, Tube length vs. yield and outlet pressure, shows minimum length constraint at 1.1 atm
python -m pytest tests/ -v31 tests, all passing.
Power Law (empirical, fitted to experimental data at 523 K):
R_HCHO = k(T) · [CH₃OH]^0.8742 · [O₂]^0.1124 · [H₂O]^-0.4858
Limitation: Does not account for surface adsorption, systematically overpredicts conversion, especially at high temperatures. Risk of suggesting unsafe operating temperatures that could lead to reactor runaway.
LHHW, Langmuir Hinshelwood Hougen Watson (Deshmukh et al. 2005):
α · k_MeOH · K_MeOH · P_MeOH · K_O₂ · P_O₂^0.5
R_HCHO = ──────────────────────────────────────────────────────
(1 + K_MeOH·P_MeOH + K_H₂O·P_H₂O)(1 + K_O₂·P_O₂^0.5)
Advantage: Captures competitive adsorption (methanol/water compete for active sites), surface saturation at high methanol concentrations, and temperature dependent adsorption equilibria. More accurate, particularly at high temperatures and adiabatic conditions.
dn_i/dz = (ν₁ᵢ r₁ + ν₂ᵢ r₂) · Ac · (1−ε) · ρ_cat
- Isothermal: heat duty
dQ/dz = −ΔHr · r₁ · ρ_cat · Ac · (1−ε) - Adiabatic:
dT/dz = −ΔHr · r₁ · ρ_cat · Ac · (1−ε) / (F_tot · Cp_mix)
dP/dz = −1.75 G² (1−ε) / (Dₚ ρ ε³)
Outlet pressure must remain ≥ 1.1 atm for downstream separation.
| Parameter | Value |
|---|---|
| Feed composition | 11% CH₃OH, 6% O₂, 3% H₂O, 80% N₂ |
| Inlet T | 430 K |
| Inlet P | 1.6 atm |
| Min outlet P | 1.1 atm |
| Tube diameter | 20 mm |
| Optimal T (isothermal) | 640 K |
| Optimal tube length | 0.5 m |
| Number of tubes | 23,000 |
| Target production | 100 t/day HCHO |
| HCHO yield | 95.7% |
| Selectivity | 96.5% |
The feed oxygen concentration (6 vol%) is below the Lowest Oxygen Concentration (LOC = 10 vol%) for methanol combustion. This means flame propagation is inherently inhibited, even though the methanol concentration (11%) falls within its flammability limits. High N₂ dilution (80%) provides an additional safety buffer.
- Deshmukh, S.A.R.K., Annaland, M.V.S. & Kuipers, J.A.M. (2005). Kinetics of the partial oxidation of methanol over a Fe/Mo catalyst. Applied Catalysis A.
- Fogler, H.S. Elements of Chemical Reaction Engineering. 5th ed.
- Ergun, S. (1952). Fluid flow through packed columns. Chem. Eng. Prog.
MEng Chemical Engineering, Imperial College London (Group 20, 2025)